A stable and efficient adaptive notch filter for direct frequency estimation

We investigate the problem of direct frequency estimation. A new adaptive algorithm is proposed based on G. Li's earlier work (see IEEE Trans. on Sig. Processing, vol.45, no.8, p.2001-9, 1997), where the constrained pole-zero notch filter was cascaded and each stage was implemented with controllable realization. It is well known that the performance of adaptive filters is strongly related to how the filters are parametrized and implemented. The normal based realizations have some nice numerical properties. In the proposed algorithm, each subfilter is parametrized with its notching frequency and implemented with a normal realization. Compared with Li's earlier structure, this one makes the algorithm more robust, such that the stability can be ensured automatically no matter whether the algorithm is implemented with or without infinite precision. Simulations show that the adaptive algorithm with the proposed structure also has better convergence behavior. Application of this algorithm to speech processing is also discussed.

Adaptive notch filter by direct frequency estimation

This paper proposes a multiple adaptive notch filter with the p‐th power average of the estimated error E[ep(n)] ‖as the cost function. The adaptive filter consists of a cascade connection of second‐order adaptive notch filters composed of the allpass filters. In general, the elimination bandwidth of the notch filter is desirably small from the practical point of view. However, as the elimination bandwidth is set smaller, the convergence speed of the tap coefficients of the adaptive filter becomes much slower. From the point of view of convergence theory, the radius of the pole of the second‐order allpass filter needs to be close to 1, so that the elimination bandwidth must be extremely small. Convergence speed must be sacrificed due to the practical and theoretical points of view. In this paper, an adaptive notch filter is studied in which the elimination bandwidth of the notch filter is designed small while the gradient of the tap vector of the cost function used in the adaptive algorithm is made effectively equal to the case in which the elimination bandwidth is rather large. In this way, realization of a multiple adaptive notch filter with a high convergence is possible. The absolute value of the transfer function of the notch filter is close to 0 near the elimination frequency while it is close to 1 at other frequencies. Hence, by setting the power of the absolute value larger, the elimination bandwidth becomes larger and the smoothness near the elimination frequency is increased. By means of the gradient algorithm with a cost function E[ep(n)], this property can be utilized so that excellent convergence speed and steady‐state characteristics can be obtained. Finally, verification of the analytical results and comparison with the conventional method are carried out by computer simulation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(8): 1–8, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10162

This paper presents efficient low-power adaptive filter architecture for electroencephalogram (EEG) signal and epileptic seizure detection using recurrence quantification analysis (RQA). The preprocessing of EEG is done using notch, wavelet and adaptive filter. The comparison of signal-to-noise ratio of the filter outputs proves that the adaptive filter provides better performance and a parallel interleaved sample of direct form adaptive FIR filter architecture is implemented and low-power issues are addressed. An innovative compressor-based addition technique is utilized in the filter implementation to reduce the area and power consumption. The design is developed using Verilog HDL and mapped to 65-nm technological node. The power results are compared with conventional architecture of adaptive filter. The major advantage of choosing RQA is that it provides better information even for short non-stationary and nonlinear signals where other methods fail to provide good results. And it requires no conventions about data set size or dispersal of the data. The algorithm is applied on epileptic EEG signal from CHB-MIT database. The RQA measures are determined from the recurrence plot, its performance is measured in terms of sensitivity and specificity as 97.4 and 93.5 %, respectively, and leakage power is reduced to 10 %.

Introduction: When creating such information processing systems as Doppler speed and acceleration meters, moving target selection systems, radio altimeters with frequency modulation of the carrier signal, or coordinated devices for detecting and evaluating the parameters of objects, the developers use a variety of filters synthesized by the methods of bilinear z transformation and invariant impulse or transient characteristics. Purpose: Creating a technique for synthesizing discrete filters using differential equations of their counterpart continuous filters. Results: In the general form, in order to derive difference equations describing the operation of the discrete filters you synthesize, the differential equation derivatives are replaced by their counterparts in the form of difference equations. The weight coefficients for filters of various orders are listed in a table. The calculation has shown that when the discreteness period is chosen properly, the frequency characteristics of the synthesized filters practically coincide with those of the corresponding continuous filters. As an example, difference equations for low and high frequency filters, oscillatory links, notch filters and selective filters were obtained on the basis of known differential equations of the counterpart continuous filters which can be used in measuring the speed, range or angular position of an object. Practical relevance: The proposed technique allows you to create a variety of linear systems, such as low or high frequency filters, oscillatory links, notch or selective filters used in various information processing systems.

It is well known that guaranteeing the stability of a recursive digital filter is the most important issue in the filter design process. The main objective of this paper is to present a new unity-bounded function for designing stable recursive digital filters. As an application example, this paper applies the new unity-bounded function to the design of odd-order recursive notch filters with controllable notch width, while the notch frequency is fixed. Notch filters with various notch widths are designed, and stability triangles are used to verify the stability of the designed odd-order notch filters using the proposed unity-bounded function.

Second-order notch filters (NFs) with constant coefficients are often used as part of feedback controllers in grid-connected power conversion systems to prevent unwanted harmonic content polluting the closed control loops. In practice, the value of the mains frequency resides within a certain known range rather than remaining constant. Hence, the correct selection of NF coefficients is crucial for ensuring that the desired performance is maintained within the whole expected mains frequency range. Bilinear transformation (BLT) with notch frequency prewarping is often adopted to convert an NF from a continuous to a digital form. While accurately preserving the notch frequency location, the method reduces the filter bandwidth. As a remedy, BLT with both notch frequency and damping ratio prewarping may be employed. Nevertheless, some inaccuracy remains under low sampling-to-notch frequency ratios. This technical note demonstrates that the issue may be solved by prewarping the boundary values of the expected harmonic frequency range rather than the notch frequency and/or damping factor before applying the BLT. Simulation results accurately support the presented issue and proposed solution.

Least Mean Square (LMS) algorithm is the most popular adaptive algorithm (AA) for realization of a digital adaptive filter (AF). In digital implementation of AF, finite word length hardware is unavoidable. This finite precision (FP) effect on the performance of the AF is crucial in the sense that, if proper word length is not used the performance in terms of the mean square error (MSE) of the filter degrades substantially. In this paper, a new approach based on the probability theory is used to analyze the FP effect of the LMS based finite impulse response (FIR) AF. An expression of the adaptation failure in terms of word length and the step size is derived. Simulation study of a FP LMS adaptive equalizer is carried out to demonstrate and verify this effect. This study provides an important guide-line to the designers for selecting the optimum word length for a specific application for a given MSE criterion.

A technique for designing a sparse FIR notch filter is presented. First, a sparse property of the ideal notch filter, whose notch frequency has the form (q/2p)/spl pi/ is derived, where p and q are coprime integers. Then, the Lagrange multiplier method is used to obtain the coefficients of the sparse notch filter which is optimal in the least-squares sense. Next, a design example is presented to demonstrate the effectiveness of this approach. Finally, a sparse notch filter is applied to eliminate the 60 Hz powerline interference superimposed on the electrocardiogram signals.

A narrowband active vibration control algorithm with frequency estimator based on lattice notch filter is proposed to suppress the primary signal with multi line spectra. A adaptive iir (infinite impulse response) lattice gradient notch filter was adapted to estimated the frequency of the multi-harmonics buried in the primary signal, then the reference signal is filtered by the adaptive band pass filter. With the reference signal filtered by the adaptive band pass filter, active control algorithm is implemented. Simulations of the frequency estimation of the multi-sinusoidal signal are conducted and simulation results confirm that the proposed algorithm could achieve effective performance when the frequency of the primary disturbance is unknown. Active control of vibration has finds a lot application such as fans, engines, and air conditioners in nowadays. The basic concept of active vibration control is to suppress the primary disturbance with the secondary force which is of same amplitude and opposite phase. Signals generated by the rotating machines such as fans, diesel engines, and air conditioners is characterized with discreet frequency which cause damage to operator in the working environment. Narrowband active vibration control (NAVC) is an effective method to suppress such vibration with multi-line spectra. The application of NAVC has been implemented taken into applications since 1970's. A lot of algorithms have been proposed for suppress the primary disturbance with multi-spectral. There exists two families of algorithm in AVC system, which composed of filtered-X least mean square (FXLMS) algorithm and filtered-X recursive least square algorithm (FXRLS). Due to its simplicity and implementation efficiency, FXLMS algorithm is the most popular adaptive algorithm to suppress the primary disturbance compared to FXRLS algorithms. In the application of NAVC systems, the performance of NAVC systems is directly correlated with the reference signal and the primary signal. NAVC algorithm could not achieve effective performance if the correlation between the primary signal and the reference signal is weak. Frequency estimation of the primary signal is an effective method to adapt to improve the relativity between the reference signal and the primary signal. To estimate the frequency of a sinusoidal signal, a number of algorithm has been proposed to exploit the predictable nature of sinusoidal primary disturbance and characterize the frequency of the sinusoidal primary disturbance, such the Kalman algorithm, music, FFT (fast Fourier transform), etc. such method could be capable of tracking nonstationary or slowly-varyin g primary signals. However, they have some shortcomings in the application of NAVC systems. a lot of Kalman-based algorithms have been proposed for the frequency estimation of the sinusoidal signal in many applications such as the electrical power system, however, it requires much more computation burdens which is much more complicated compared the other algorithms. FFT methods have been proposed in the past to estimated the frequency of the primary signal, but it is has been found that the estimated result could not be accessed effectively in real-time of AVC system. Adaptive notch filter has been proposed for the frequency estimation of the sinusoidal signal in a lot of applications. Adaptive lattice filter shows much more stability and performance compared to the bilinear adaptive notch filter. In this paper, the adaptive lattice notch filter is introduced into an adaptive vibration control system to estimate the frequency of synthesized desired signal. Then, the reference signal is generated to suppress the primary vibration in the active vibration control system.

This paper deals with a state-space approach for adaptive second-order IIR notch filters with constrained poles and zeros. A simplified adaptive iterative algorithm is derived from the gradient-descent method for minimizing the mean-squared output error of an adaptive notch filter. Stability and parameter estimation bias are analyzed for the adaptive iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch filter and parameter-estimation bias analysis.

The task of removing sinusoidal components from observed signals can be accomplished by using a notch filter with a specific attenuation at a particular frequency. In some applications, however, such as acoustic feedback control, the frequency at which attenuation is required is unknown and possibly time-varying, and hence an adaptive notch filter is a more appropriate solution. Transitioning from a fixed notch filter to an adaptive one is by no means trivial and involves the understanding of a range of digital signal processing (DSP) topics from pole-zero placement techniques for designing infinite impulse response filters to optimal and adaptive filtering algorithms. In the signal processing algorithms and implementation graduate course taught at KU Leuven (Belgium), we study the design of an adaptive notch filter, which is based on a constrained biquadratic IIR representation, andwhose parameters are updated using a least-mean-square algorithm. Students also have to implement the algorithm on a 16-bit DSP TMS320C5515. In this presentation, we will discuss the design and implementation challenges of this adaptive notch filter and how it serves as an illustrative example/homework problem where several aspects of DSP are interwoven.

Adaptive filters are prevalent in many real‐time signal processing applications. Many adaptive algorithms already exist, but most of them assume white Gaussian noise as disturbance. However, for many applications such as electrocardiogram, foetus heart rate measurement, low frequency atmospheric noise, underwater acoustic noise and signal measurement in instrumentation, the impulsive noise is more common. This study presents a modified robust mixed norm (MRMN) adaptive filter algorithm robust to impulsive noise with higher convergence rate and lower steady state error (SSE). MRMN adaptive filter algorithm has been simulated using Matlab and Xilinx system generator high level synthesis tool and a significant improvement in SSE and convergence speed is obtained compared with the existing adaptive filter algorithms for similar specifications. The proposed algorithm is also described using VHDL and synthesised using Xilinx synthesiser tool in order to implement on field‐programmable gate array (FPGA). The FPGA post route and place implementation results show nearly 90% reduction in resource utilisation and nearly 2.6 times improvement in clock frequency as compared with the existing FPGA based implementation for similar specifications.

Straightforward methods for the design of digital notch filters are presented. The design method is based on setting a zero of the filter at a notch frequency and placing a pole in its neighborhood such that the notch width is narrow enough while keeping the group delay of the filter sufficiently flat. A technique for efficient and well-behaved implementation with fixed-point signal processors is advanced, based on the use of quantization error feedback for roundoff noise reduction. The design approach is illustrated with numerical examples, and an assembly-language program for the family of TMS320 signal processors is provided. >

An adaptive digital notch filter is considered for 50/60 Hz line frequency signal processing. An adaptive algorithm allows tracking of the main frequency component such that the notch frequency is the only changing parameter. Since the power line frequency is known to within a narrow tolerance band, it is possible to apply soft or hard limiting on the notch frequency. Soft and hard limiting are compared for Laplacian noise, and the effect of filtering is investigated for a signal with strong harmonic contents.